Method of thermally drawing structured sheets

ABSTRACT

A method of drawing a material into sheet form includes forming a preform comprising at least one material as a large aspect ratio block wherein a first transverse dimension of the preform is much greater than a second transverse dimension substantially perpendicular to the first transverse dimension. A furnace having substantially linearly opposed heating elements one spaced from the other is provided and the heating elements are energized to apply heat to the preform to create a negative thermal gradient from an exterior surface along the first transverse dimension of the preform inward toward a central plane of the preform. The preform is drawn in such a manner that the material substantially maintains its first transverse dimension and deforms across its second transverse dimension.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application Ser.Nos. 61/768,506, filed Feb. 24, 2013; 61/768,507, filed Feb. 24, 2013;61/914,606, filed Dec. 11, 2013; and 61/914,616, filed Dec. 11, 2013,the disclosures of which are hereby incorporated herein by reference intheir entireties.

FIELD OF THE INVENTION

The present disclosure generally relates to apparatuses and methods forthe drawing of materials from a preform. More particularly, the presentdisclosure relates to a method of thermally drawing an elongate sheetfrom a preform wherein the material is maintained dimensionally constantin a first transverse dimension and reduced in a second transversedimension.

BACKGROUND OF THE INVENTION

Techniques for heating, and subsequently drawing, glass into fine fibershas been known for millennia. It was, however, during the 1930s whenthis technique was first introduced into the textile industry. Asfurther explained below, this technique was employed later, during the19th century, to manufacture glass optical fibers.

Light guidance in transparent pipes and water streams historicallyinspired the use of optical fibers for light transmission. The lightguiding process using the total internal reflection was firstdemonstrated by Daniel Colladon and Jacques Babinet in Paris during theearly 1840s. It found applications such as illumination in dentistry,image transmission and internal medical examination early in the 20thcentury. Later, during the 1920s, the concept of modern glass fiberswith a glass core and a lower index cladding for a more suitable indexguiding was introduced. Low-index oils and waxes were mostly used toproduce the lower-index cladding. During the 1950s, University ofMichigan undergraduate student Lawrence E. Curtis produced the firstglass-core fiber having glass cladding for minimizing the interferenceof guided light with the surrounding environment. Advances in the fiberfabrication process combined with the proper choice of glass materialsrendered the optical fibers as feasible tools for long-distance opticaltelecommunications, as well as many other applications such as sensingand imaging. During the 1990s, micro-structured fibers and photoniccrystal fibers were developed wherein the guiding mechanism was basedupon light diffraction from periodic structures in the fiber. It wasfound that photonic crystal fibers could potentially transmit higherlight power and would give the possibility of dispersion adjustmentbased on structure design. In recent years, a new class of fibers(so-called multi-material fibers) emerged based on thermal co-drawing ofmultiple types of materials all having thermally and mechanicallycompatible properties. This new class of fibers enabled the introductionof novel functionalities (i.e., not limited to optical lighttransmission). For example, one novel expanded functionality includedfibers with semiconducting glass and metal electrodes integrated into asingle fiber for light detection applications. The field ofmulti-material fibers recently expanded even further to includepiezoelectric fibers and multi-material fibers for structuredmicrosphere and nanosphere fabrication.

Throughout the history of fiber development, thermal fiber drawing hasbeen the most popular and the most successful fabrication method.Simplicity and speed of thermal fiber drawing made opticaltelecommunication an economically viable technology. The circularlysymmetric geometry of optical fiber fabrication was indeed inspired bythe natural shape of water streams and glass fibers that were producedthrough heating and pulling of glass.

In the fiber drawing process, softened material has the tendency toround up into fibers having a circular cross-section to minimize thesurface free energy under surface tension. However, in the longitudinaldirection, the tension along the fiber that is produced by theintentional pulling process, dominates the surface tension and leavesthe fiber longitudinally elongated. During the pulling process, materialis maintained at or about the softening temperature for a (brief) periodof time adequate to stretch it into a fiber. It is then gradually cooledto solidify the stretched form that is called a fiber. This is the fiberfabrication process that has been used for centuries in the textileindustry and for decades in the field of optics. In recent years, fibershaving non-circular cross-sectional areas have been created by giving anasymmetric geometry to the fiber preform and trying to maintain thatgeometry by not overly heating the fiber during the drawing process. Itis possible to maintain non-circular structures by not giving thematerial enough freedom (low viscosity) and time to round up to acircular shape. Fibers made using this method—having hexagonal, square,rectangular and even D-shaped cross-sections—have been reported forvarious applications. With regard to all fibers of different materialsfor various applications over decades, the circular symmetry of fiberpreform heating has allowed for equal scale reduction in both transversedirections (i.e., height and width) across the fiber. This results inmaintenance of the aspect ratio of the preform in the final drawn fiberby allowing equal shrinkage in both transverse directions

In conventional fiber drawing methods, and as illustrated in FIG. 1, afiber preform 110 is placed in a tubular (or similar) furnace 140wherein a heating element 142 surrounds the preform 110 in a manner thatprovides uniform heating about the preform 110. The furnace beginsheating and softening the materials from the outermost layers to theinnermost layers of the preform 110. As a result, there is always arelatively large temperature (and hence viscosity) gradient across thefiber preform 110 in the radial direction ‘B’ (transverse to thelongitudinal axis ‘A’). The middle of the preform 110 (coinciding withthe center of the furnace 140) has the highest viscosity, while theouter layers have relatively lower viscosities. This viscosity gradientacts to force the material to flow toward, and stretch from, the centerof the preform 110, where the temperature is lowest and the viscosity ishighest. This can be confirmed by dislocating the preform 110 in such amanner that its center no longer coincides with the center of symmetry(or more accurately the coldest point) of the furnace 140. In this case,the material flow and stretching occurs from the location of the lowestfurnace temperature that is not at the center of the preform 110. Thisis commonly referred to as “asymmetric fiber pulling,” which is notdesired for most fibers. To minimize this problem most fiber drawmachines have automatic centering features that align the preform 110with the center of furnace 140.

If the preform does not have a cylindrical shape, it will still shrinkalmost uniformly in both transverse directions and will maintain theoriginal shape in a smaller scale, unless temperature is too high andtherefore viscosity is too low. In that case, the material has atendency to minimize its free energy under surface tension. This willdeform the fiber's cross-section towards a circular one.

However, the use of a furnace that supplies a uniform thermal gradientabout 360 degrees of a preform limits the shapes that can be drawn.Therefore, a method of applying thermal gradients to facilitatecross-sectional shapes not possible with circular heating is needed.

SUMMARY OF THE INVENTION

The present disclosure is generally directed to a method of drawing amaterial into sheet form. In one embodiment, the method includes forminga preform comprising at least one material as a large aspect ratio blockwherein a first transverse dimension of the preform is greater than asecond transverse dimension substantially perpendicular to the firsttransverse dimension. For example, the present invention may be used toproduce elliptical fibers from a circular preform, or a rectangularfiber from a square preform. A furnace having substantially linearlyopposed heating elements one spaced from the other is provided and theheating elements are energized to apply heat to the preform to create anegative thermal gradient from an exterior surface along the firsttransverse dimension of the preform inward toward a plane of thepreform, in accordance with one embodiment. In one embodiment, thepreform is drawn in such a manner that the material may substantiallymaintains its first transverse dimension and deforms across its secondtransverse dimension.

These and other features, aspects, and advantages of the invention willbe further understood and appreciated by those skilled in the art byreference to the following written specification, claims and appendeddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described, by way of example, with referenceto the accompanying drawings, where like numerals denote like elementsand in which:

FIG. 1 presents an isometric schematic view of a prior art tubularfurnace for heating and drawing a fiber from a cylindrical preform;

FIG. 2 presents an isometric schematic view of a furnace which suppliesa thermal gradient in a linear fashion and embodying the presentinvention, wherein the thermal gradient is applied to opposing widths ofa rectilinear preform for drawing a sheet, in accordance with oneembodiment;

FIG. 3 presents an isometric view of a rectilinear preform illustratingthe applied thermal gradient, in accordance with one embodiment;

FIG. 4 presents a cross-sectional view of a preform having a singlecentrally located element of a secondary material, in accordance withone embodiment;

FIG. 5 presents a cross-sectional view of the preform of FIG. 4 duringthe drawing process, in accordance with one embodiment;

FIG. 6 presents a cross-sectional view of a multi-layered preform beingdrawn down to a sheet having multiple thin layers, in accordance withone embodiment;

FIG. 7 presents an isometric view of a preform having an embeddedpatterned insert modified in at least one dimension to facilitatedrawing into a desired finished pattern, in accordance with oneembodiment;

FIG. 8 presents a cross-sectional view of a preform having a pluralityof vertically aligned secondary elements within a primary preform block,in accordance with one embodiment;

FIG. 9 presents a cross-sectional view of the preform of FIG. 8 duringthe drawing process, in accordance with one embodiment;

FIG. 10 presents a cross-sectional view of a preform having fourvertically-aligned secondary element within a primary preform block, inaccordance with one embodiment;

FIG. 11 presents a cross-sectional view of the preform of FIG. 10 duringthe drawing process and showing the deformed secondary elements in theresultant drawn sheet, in accordance with one embodiment;

FIG. 12 presents an isometric view of a preform having a plurality ofparallel vertical secondary elements and differently shaped outertertiary elements in the drawing process, in accordance with oneembodiment;

FIG. 13 presents a cross-sectional view of the preform of FIG. 12 duringthe drawing process illustrating the drawn sheet including the deformedsecondary and tertiary elements, in accordance with one embodiment;

FIG. 14 illustrates one method to avoid delamination and separation ofcomponents in a multi-material film in accordance with one embodiment;

FIG. 15 illustrates one method to avoid delamination and separation ofcomponents in a multi-material film in accordance with one embodiment;and

FIG. 16 illustrates a method for asymmetric drawing in accordance withone embodiment.

Like reference numerals refer to like parts throughout the various viewsof the drawings.

DETAILED DESCRIPTION OF THE PREFERRED IMPLEMENTATIONS

The following detailed description is merely exemplary in nature and isnot intended to limit the described embodiments or the application anduses of the described embodiments. As used herein, the word “exemplary”or “illustrative” means “serving as an example, instance, orillustration.” Any implementation described herein as “exemplary” or“illustrative” is not necessarily to be construed as preferred oradvantageous over other implementations. All of the implementationsdescribed below are exemplary implementations provided to enable personsskilled in the art to make or use the embodiments of the disclosure andare not intended to limit the scope of the disclosure, which is definedby the claims. For purposes of description herein, the terms “upper”,“lower”, “left”, “rear”, “right”, “front”, “vertical”, “horizontal”, andderivatives thereof shall relate to the invention as oriented in FIG. 2.Furthermore, there is no intention to be bound by any expressed orimplied theory presented in the preceding technical field, background,brief summary or the following detailed description. It is also to beunderstood that the specific devices and processes illustrated in theattached drawings, and described in the following specification, aresimply exemplary embodiments of the inventive concepts defined in theappended claims. Hence, specific dimensions and other physicalcharacteristics relating to the embodiments disclosed herein are not tobe considered as limiting, unless the claims expressly state otherwise.

In one exemplary implementation of the invention, a furnace 210 is shownin FIGS. 2-3 wherein a rectilinear, or large aspect ratio, preform 240is illustrated being drawn into a longitudinally extending sheet 244.Furnace 210 includes thermal elements 212 extending along a width of thepreform 240. The opposed thermal elements 212 produce a thermal gradientconfiguration according to the opposed gradients “C” as illustrated inFIG. 3.

A geometry of material drawing may be considered as a linear counterpartof conventional fiber drawing. A linear symmetry may be maintainedduring the drawing process with the preform 240 of large aspect ratio tocreate a film or sheet 244 as opposed to known circular fibers. Theheating geometry is linear as evidenced by thermal elements 212. Thermalelements may be implemented as a combination of multiple lines ofheating elements controlled separately. One embodiment may include threerows of heaters: top, middle and bottom. A person of ordinary skill willrecognize that the number of heating elements can be increased ordecreased. Multiple heaters may be used to preheat the material beforeit enters the hottest zone of the furnace and to gradually bring thematerial to room temperature after it leaves the hottest zone.Pre-heating helps to accelerate the process by preparing the materialfor faster softening before it enters the hottest zone where actualdeformation and drawing takes place. In one embodiment, post-heating toa temperature intermediate between the hottest zone and the ambienttemperature takes place to avoid cracks and fractures due tothermal/mechanical shock. Depending on the materials used for thepreform, one may need to increase the number of heaters in order togradually cool the films down before exposing them to the ambient. Thedimensions of the preform 240 are such that heat distribution gains alinear symmetry across the preform. Size reduction (shrinkage) of thepreform 240 to the sheet 244 in the two transverse dimensions isunequal. The preform 240 begins with a thickness of “t1” and is reducedto “t2” as a result of the opposed thermal gradients “C” appliedlinearly along the width “w1” of the preform 240. Since the ends 241 ofthe preform 240 are not subjected to a thermal gradient acting normal tothe end surface, the post-drawn width “w2” of sheet 244 is substantiallythe same as the pre-drawn width “w1” of the preform 240 in suchconditions so that little to no shrinkage occurs in one transversedimension (width) except for small shrinkage at the edges of the preformwhere linear symmetry is broken and full shrinkage happens in the othertransverse direction (thickness). The establishment of a largetemperature (and viscosity) gradient across one dimension of the preform240 utilizing the heating geometry of the invention, limits shrinkage toonly one transverse dimension as opposed to conventional fiber drawingwhere the viscosity has a circular symmetry about the preform with aradially inward directed gradient.

By eliminating a viscosity gradient in one dimension and applying alarge viscosity gradient in the other dimension sheets are produced byshrinking a large aspect ratio preform 240 in only one transversedimension. In the same way as maintaining internal structures in fibers,structures are maintained in thermally drawn sheets made with thismethod. However, just as the whole preform does not shrink in the secondtransverse direction, neither does any preform structure shrink in thatsecond transverse direction (edges are the exceptions—structures closeto the edges experience some deformation in both directions). In thethird (longitudinal) direction, which is the pulling direction, theentire preform 240 is stretched, thereby producing the sheet 244.

In such linear heating schemes, even perfect cylindrical preforms can bedrawn to elliptical fiber. Similarly, a preform with squarecross-section can be drawn into a rectangular fiber. Such a linearheating scheme will change the aspect ratio of the preform during thedrawing process because size reduction is different in two orthogonaltransverse directions.

A furnace can have multiple vertical zones in order to controlpre-heating, melting, and post-cooling of the preform material. Preformmaterial can be pre-heated with a top heating zone to below thesoftening point, then heated to the maximum required temperature fordrawing, and finally gradually cooled down to room temperature using abottom heating zone adjusted to an intermediate temperature.

Temperature gradient “C” does not have to be symmetric across thethickness T1 of the slab-like preform. The material will be pulled fromthe line or point of lowest temperature. If temperature distribution issymmetric across the thickness T1, the film will be pulled from thecentral line of symmetry of the preform. Otherwise, the line of lowesttemperature will fall on one side of line of symmetry of the preformand, therefore, film will be pulled from that location instead. In caseswhere the thickness of the preform is not considerably large compared tothat of the furnace, it will be difficult to create enough temperaturegradient between outer surface of the preform (front and rear) and thecenter line of the preform. It is more practical to create a largetemperature gradient from one surface to another instead. Therefore, thefilm drawing will take place asymmetrically from a line closer to onesurface than to the other.

This technique has many advantages that no other existing methodprovides. Sheets can be made in very large scales. Just like a fiberpreform that can produce kilometers of fiber when drawn, the slab-likepreform 240 having a large aspect ratio and drawn with this new methodcan also produce very long lengths of sheets. As long as the heatingsymmetry is maintained, the process can be utilized to produce very widesheets. This method can be applied to a wide variety of materials. Thatis, a wide variety of materials can be used for assembly of preforms andfilm drawing. Any material that shows a softening temperature, a glasstransition temperature or a smooth variation in viscosity as a functionof temperature can be implemented in this process. Examples arethermoplastic polymers, all types of glasses, amorphous materials thatcan be stretched when heated, and metals. In one embodiment, thepreforms have elements with matching thermal and mechanical properties.To be more specific, viscosity of elements of a multi-material preformis preferably approximately the same (within some tolerance) at a giventemperature used for the film drawing process, this, in order tomaintain structural features from the preform to the film with a fixedscaling factor. One can make films with slightly incompatible materialstoo. But the elements with lower viscosity at the working temperaturewill flow faster and more easily than others. Thus, those elements willexperience different scaling factors.

This process can be conducted at any temperature ranging from −100 C to3000 C. The processing temperature will vary depending on the materialsto be drawn. For example, if structured films of materials with meltingtemperature below zero are needed, one can conduct the process undercryogenic conditions close to the softening temperature of materials inquestion. In one embodiment, if structured films with polymers and/orsoft glasses are needed, temperatures ranging from room temperature to600 C can be used. If structured thin sheets of high-temperaturematerials such as silica glass are needed, higher temperature furnacescan be used to achieve temperature ranges 600 C-3000 C depending onmaterials.

Possible Structures and Applications

Uniform Materials

The simplest type of sheet can be a sheet with uniform material such asillustrated in FIGS. 2-3. This can be made by starting from the preform240 made of a uniform material. In one embodiment, this will result in asheet of uniform material with uniformity of the material maintained inall dimensions of the final film. This simple product can also be madein many other ways. By use of the disclosed process, molecules andelements can be stretched and aligned along the pulling direction. Anadvantage of making uniform films with this technique is that thequality and consistency of the film surface and thickness is controlledby surface tension that can be easily maintained across the width of thepreform and film as opposed to, for example, sheet extrusion where filmthickness consistency depends on the consistency of the die slit. Thismakes it difficult or practically impossible to extrude films thinnerthan a few micrometers with acceptable thickness consistency. With thisdisclosed technique even submicron films of materials can be drawnconsistently, especially if the target thin film material is supportedby layers of a secondary material in preform so that the thin film doesnot break under tension. Supporting secondary material can be athermally and mechanically matching material that can be co-drawnsimultaneously and can be removed from the thin film after drawing.

Layered Sheets

As mentioned above any structure along the pulling direction of thedrawn sheets will be stretched from the preform (slab) level to thesheet level. In one embodiment, any structure across the width of theslab-like preform will remain unchanged when viewed normally to thesheet. However, structures across the thickness of the slab-like preform(direction of high temperature gradient) will shrink down multipletimes. As shown in FIGS. 4-5, a preform 340 includes a large primaryblock 352 of a first material has embedded therein a secondary block 354of a second material. In one embodiment, the preform 340 is transformedvia application of the thermal gradient “C” during the drawing processto a thinner sheet 342 having substantially the same width as thepreform 340 with a reduced thickness and the thicknesses of the layersof the primary and secondary materials 352, 354 in substantially thesame proportion as the pre-drawn thicknesses. It is, however,anticipated that thickness ratios change slightly from the surface ofthe sheet toward the center plane (or plane of the highest viscosity) ina manner that layers closest to the center plane shrink slightly lessthan those away from that plane.

Similarly, as shown in FIG. 6, a preform 440 having parallel layers ofdifferent materials 452, 454, 456 or even identical materials withdifferent dopants may be drawn down to a relatively thin multi-layeredsheet 442 and create novel devices.

Examples of such layered devices are listed below. However, thismaterial processing method, while inclusive of, is not limited to thefollowing examples.

Bragg's Reflectors and Anti-Reflective (AR) Films—Large Scale

Interference-based thin films for selective reflection and selectivetransmission of waves (electromagnetic and/or acoustic) can be createdwith this method. It has long been known that single layers ormulti-layer stacks of optical materials with proper refractive indicescan create anti-reflective coating for numerous applications wherereflection is not desired and needs be minimized. On the other hand,thicknesses and refractive indices of the layers can be adjusted tomaximize interferometric reflection. Optical Bragg reflection may bedefined as a reflection from a periodic stack of materials withdifferent refractive indices. It was shown in late 1970s that undercertain circumstances including high refractive index contrast,omni-directional Bragg reflection could occur. Later, omni-directionalreflection was experimentally demonstrated on flat substrates withalternative high-index, low-index glass depositions. All these devicesare made using direct deposition of thin films of optical materials.Therefore, the fabrication process is relatively slow, expensive andlimited to small areas. Although deposition technologies have beendeveloped and improved for reflective and AR coating for large-areadevices such as displays, the omnidirectional and Bragg reflectors havenever been demonstrated in large areas.

The thermal sheet drawing process described herein permits a variety oflayered structures either for reflection enhancement or for itselimination. Layers of different materials can be stacked in alarge-scale slab-like preform and be drawn down uniformly to the thinfilm form. This technique makes it possible to create AR or Braggreflectors in very large areas at very low cost. In addition, since thisfabrication method is based on a top-down approach starting fromlarge-scale slab preforms, it is less sensitive to layer thicknesserrors. In other words, compared to depositing microscopic layers withhigh accuracy, it is much simpler to fabricate macroscopic layers anddraw them down to microscopic dimensions with adjusted drawdown ratio byuse of the present invention. Another advantage is that one slab preformcan give AR or Bragg reflector films for any desired wavelength rangejust by adjusting the drawdown ratio that can also be changed during onesingle draw through adjustment of drawing parameters such as filmpulling speed and tension, preform down-feed speed, and temperature.

Acoustic Interference-Based Reflector and Anti-Reflection Film

Periodic structures of high elasticity contrast (Phononic Crystals) havebeen studied theoretically and experimentally in the past decade. It hasbeen theoretically demonstrated that one-dimensional periodic structuresof high elasticity contrast materials can create omni-directional andwide-angle sound reflection for frequency ranges that depend on the sizeof the alternating material layers. In a similar fashion to the opticalAR and Bragg reflectors, the acoustic reflection and anti-reflectionsheets can be made for either sound transmission improvement or soundtransmission blocking in flat and/or flexible films. This can happen bysatisfying the conditions for either constructive or destructiveinterference between the acoustic waves reflected off or transmittedthrough periodic layers. The present thermal sheet drawing method can beemployed in the same way explained above for the optical AR and Braggreflectors to make acoustic reflection and anti-reflection possible inlarge-area thin sheets. Such structures can be made using thermoplasticpolymers and low-temperature glasses (such as Chalcogenide glasses,Chalcohalide glasses and other similar compositions) having verydifferent elastic constants over a wide range. This technique inconjunction with another technique (hybrid drawing of incompatiblematerials, disclosed in U.S. Prov. Pat. App. No. 61/768,507) permitsalternating layers of metals and polymers or glasses to utilize the lowelasticity of metal layers in high contrast with the high elasticity ofpolymers.

Chirped Layered Structures

This technique permits the fabrication of chirped structures of anyarbitrary chirping profile for both optical and acoustic applications.The only difference being the fabrication of the slab-like preformincludes the scaled-up version of the desired structure to fulfilleither optical or acoustic function as desired and designed.

Sheets with Complex Refractive Index Profiles such as Rugate Filter

This technique can be used for fabrication of sheets with arbitrarycomplex refractive index profiles such as Rugate filters in the depth ofthe sheet. Multiple materials or multiple variations of the samematerial (doped or un-doped by guest dopants) can be arranged andstacked with various thicknesses in macroscopic level to createarbitrary index fluctuations across the thickness of the preform. In oneembodiment, the drawn sheet will therefore replicate the same indexvariation as a function of position in the depth of the drawn sheets,but in a much smaller scale.

Refractive index and other properties of layers for such complex(gradient-index) structures for optical and/or acoustic applicationsdescribed above can be fine-tuned in several ways. The term “refractiveindex” may refer to a complex refractive index (with real and imaginarycomponents) which is a combination of absorption and real refractiveindex. Addition of micro- or nano-scale particles of very low or veryhigh refractive index glasses or crystals (such as TiO₂) with variousconcentrations may be used to adjust the effective refractive index ofmaterials such as polymers. Another method is additions of inorganicnano-scale semiconducting particles (quantum dots) whose refractiveindices are usually much higher than that of typical polymers. Quantumdots can be mixed uniformly with polymers since organic compounds areusually attached to the particles for better solubility in chemicalsolvents. Addition of any such dopants (guests) may change theabsorption and refractive index of the host polymeric material atdifferent portions of the light spectrum. Such films can be used aswavelength-selective window films, light filters, etc., withcustomizable reflection, transmission and absorption spectra.

Capacitors or Dielectric Barriers—Large Scale

Large-scale capacitors can be made by adding conductive layers separatedby dielectric materials to the preform. Such capacitors or devices withdielectric barrier layers can alternatively be made through laminationof thermally drawn films on conductors. Another alternative is to coatconductors (anodes and cathodes) on thermally drawn films with highthickness consistency. Conventional methods have difficulties withmaintaining uniform thickness of the dielectric material across largeareas. Thin films a few microns thick are usually made by conventionalfilm extrusion methods and are sandwiched between the conductive metalfilms. The thickness consistency of film extrusion for such thin filmsof only few microns is usually very poor. Therefore, only relativelysmall width films can be extruded and used successfully for thisapplication. Utilizing the current drawing process the thickness iscontrolled by the drawing process parameters such as temperature andspeed. This allows a much higher level of control and consistency.

To go one step further, the capacitors may be produced with theelectrodes and dielectrics all during a single draw process. Conductivematerials that are compatible with the drawing process can be used.Metal conductive thin films of high conductivities can also benon-thermally fed into the thermal drawing process according to thehybrid drawing of incompatible materials disclosed separately.

A Display Application

Slab preform and therefore drawn sheets may include separate or mixedlayers with three types of luminescent materials mixed in them.Luminescent materials can be selected to emit Red, Green and Blue (RGB)colors. Luminescent materials can be organic dyes, quantum dots,organic/inorganic compounds, inorganic micro- or nano-particles such asmicro-crystals with phosphors. Each of the three luminescent materialscan be addressed (excited) with a distinct wavelength of light. Then,each point on such a drawn sheet can be addressed simultaneously byincident beams of light (i.e., laser beams) with adjusted relativeintensities to generate desired amounts of red, green and blue forarbitrary color generation. This can create a large-scale, flexibledisplay that can be addressed with existing fast-switched laser beamsteering systems with three lasers to create images on the displaysheet. For this application rare-earth and phosphor doped micro-crystalsare ideal because the low-intensity ambient light cannot excite them.Only higher-intensity laser beams can excite their emission. This can beused as large-scale flexible outdoor/indoor displays with very highcontrast and visibility.

Patterned Sheets Made with Post-Processing of Drawn Sheets

With the disclosed process large-scale, flexible sheets can be thermallydrawn with either uniform or patterned layers of materials that canundergo changes in their properties with post-processing by applicationof light, electric field, magnetic field, electric current, heat, etc.There are several classes of materials that can experience changes intheir properties including (but not limited to) electrical, optical,acoustic, and magnetic when exposed to one or many of the stimulimentioned above. To name a few examples: phase change chalcogenideglasses that are widely used for writable, re-writable memories;monomers that polymerize under light or heat exposure; organic materialssuch as azo-benzene dyes that experience photo-induced isomerization,birefringence, dichromatism, photochromatism, etc.; Electro-chromaticmaterials that show spectral changes in their response to electriccurrent can similarly be integrated. Micro- and nano-particles can bemixed with the matrix material of the preforms so that they areaddressed by external stimuli after sheet drawing in order to inducechanges in their properties. An example can be metal nano-particles thatundergo photo-induced changes. Another example is rare-earth dopedmicro- or nano-crystals with single-photon or two-photonabsorption/emission properties.

Generated patterns can be temporary, permanent, erasable and/orre-writable. They can be used for writing circuits of various types forelectrical (i.e. antenna), photonic (i.e. optical waveguide), magnetic,acoustic, or mixed functionality. They can also be used as a way ofstoring information on thin flexible surfaces either in one single layeror in multiple layers of material in the same sheet. This is similar tothe information storage mechanism on CDs and DVDs but in larger sizesand several more layers to increase the data storage capacity.

3D Photonic/Photonic Crystal Structures

As explained above optical and other properties of some materials can bemodified by external post-processing. If the initial sheet before thepost processes is a multilayer stack with high contrast in theirproperties, one- or two-dimensional patterns written on the sheets maytransform the one-dimensional periodic structures into two- orthree-dimensional periodic structure, respectively, in flexible form andlarge scales. This may be employed for fabrication of the largestphotonic crystal structures.

Patterned Preform to Patterned Sheet Direct Pulling

As discussed above, structures in the preform will shrink in onedimension (across the slab preform thickness), in accordance with oneembodiment. They will remain unchanged in the transverse directionacross the width of the preform and will be stretched along the drawingdirection. Therefore, patterned sheets can be designed and made with thedesired patterns incorporated into the preform. In a simplified formand, as shown in FIG. 7, as an exemplary implementation, a patternedsheet 542 can be formed having a finished thickness (t2) with anembedded finished pattern material 556 by, prior to drawing, embedding adesired structure 554 within a primary material 552 of the preform 540having a larger scale pre-drawn thickness (t1). Those features extendingacross the width of the sheet (w1, w2) can be made with the same scalein the preform. Finally, stretch in the drawing direction may becompensated by proper design and adjustment of the dimensions in thepreform 540. An example of such structure is a sheet with crossedconductive electrodes to generate a two-dimensional mesh grid. This canbe used in conjunction with various classes of materials for distinctapplications. Light emitting materials can also be used to generatephotons by application of electric signals. Another exemplary embodimentis a one-dimensional or two-dimensional phase or amplitude plates(films) made of materials with similar thermal and mechanicalproperties, but different light transmission or refractive indices. Suchphase plates may act as a one- or two-dimensional Fresnel zone plate orlens.

Another example is shown in FIGS. 8-9 wherein a preform 640 includes aprimary material 652 in which is embedded a plurality of verticallyaligned secondary material elements 654, 656, 658 and centered on avertical axis 646 of the preform 640. When the thermal gradient “C” isapplied (FIG. 9), the area of lowest viscosity is at the outerboundaries of the primary material 652 and the area of highest viscosityis at the central axis 646. As the sheet 642 is drawn, the secondaryelement 658 also begins to deform within the preform 640 and deformed bythe drawing process to be centrally located within the drawn sheet 642bounded on each side thereof by primary material 652.

A further example is shown in FIGS. 10-11 wherein a preform 740 includesa primary material 752 in which is embedded a plurality of verticallyaligned secondary material elements 754, 756, 758, 760 and centered on avertical axis 746 of the preform 740. When the thermal gradient “C” isapplied (FIG. 11), the area of lowest viscosity is at the outerboundaries of the primary material 752 and the area of highest viscosityis at the central axis 746. As the sheet 742 is drawn, the secondaryelements 754, 756, 758, 760 also deform along the central axis 746 toelongate within the preform 740. The secondary elements 754, 756, 758,760 are centrally located within the drawn sheet 742 along axis the 746and bounded on each side thereof by primary material 752. Thedeformation mechanics of the primary material 752 and the secondarymaterial elements 754, 756, 758, 760 are known and are provided thepre-drawing configuration of FIG. 7 such that the resultant drawn sheet742 is produced in its final desired configuration with no furtherprocessing required.

Yet another example is illustrated in FIGS. 12-13 wherein a preform 840includes a primary material 852 in which is embedded a plurality ofparallel, aligned secondary material elements 854, 856, 858. The preformcan further include tertiary side elements 860, 862 which are ofdissimilar configuration than the secondary material elements 854, 856,858. When the thermal gradient “C” is applied, the area of lowestviscosity is at the outer boundaries of the primary material 852 and thearea of highest viscosity is at the central axis 846. As the sheet 842is drawn, the secondary elements 854, 858 will deform at a lowerviscosity than secondary element 856 as a result of the difference indistances along the thermal gradient “C”. Tertiary elements 860, 862also deform at a lower viscosity than the secondary elements 854, 858 asa result of being most proximate to the highest temperature points alongthe thermal gradient “C”. The deformation mechanics of the primarymaterial 852 and the secondary material elements 854, 856, 858, 860 areknown and are provided the pre-drawing configuration of FIG. 7 such thatthe resultant drawn sheet 842 is produced in its final desiredconfiguration with no further processing required.

Single optical waveguides or waveguide arrays can be implemented infilms. Preform can include an array of one or more sections with amaterial with higher refractive index compared to the majority of thepreform material. Such sections will be elongated during the sheetsdrawing process and will form waveguides embedded in sheets. One- ortwo-dimensional arrangements of such lower index regions can be createdin preform so that the final drawn sheet encompasses a one- ortwo-dimensional array of waveguides along the sheet direction ofpulling. Such waveguide arrays may find applications in sensing wherefluctuations in the ambient can be sensed over an extended surfacecovered by such in-film waveguide through interaction of light inwaveguides and the ambient. A waveguide array in a flexible sheet/filmcan also be used for board-to-board interconnection and light signaltransport in photonic integrated circuits, especially when tight devicepackaging required connection of boards using flexible waveguides tosave space or when devices are flexible and necessarily demandflexibility of all components.

For the display application mentioned above materials used in OrganicLight Emitting Diode (OLED) technology can be used. The disclosed sheetpulling method, however, presents multiple advantages, including: (1)Large-scale displays can be made fairly easily once one preform is madeand drawn; (2) Thickness adjustment and accuracy are very critical forOLED applications because thickness of each layer is on the order of fewmicrons or even submicron. With our sheet pulling technique, thethickness of each layer will be many times larger and therefore simplerto fabricate. When the sheet is drawn all layers shrink proportionallyand submicron thicknesses can be achieved in large areas just byadjusting the sheet drawing parameters that are straightforward tocontrol; (3) Controlling dust and contamination is much easier in apreform fabrication with a small area compared to the large area of theequivalent drawn sheet. A preform can be carefully prepared under cleanand controlled ambient and drawn into sheets of extended area withoutthe concern of contamination of internal thin layers.

Other methods (mostly bottom-up methods) of making devices in flexibleform are limited in size to a few inches in each direction. The methoddisclosed herein can potentially create sheet devices in continuouspieces many times larger than existing versions (if any). This advantageapplies to all of the devices listed below, although it will not bementioned repeatedly throughout the remainder of the description.

Holey Sheets

Similar to the hollow-core and photonic crystal and band-gap fiberdrawing, sheets can also be made with hollow capillaries of arbitraryshapes and sizes running along the sheets. Transverse distribution ofthe holes may depend on applications. Any number of holes can be made inthe slab-preform in one- or two-dimensional arrangements. The preformholder can be designed in a way that allows positive or negative gasflow in the holes for controlling expansion or collapse of the holeseither independently or collectively. Various gas pressures can beapplied to different sections of the slab preform to control holesindependently. This may be considered as a linear counterpart of thewell-known photonic crystal or bandgap fibers except for the geometrywhich is changed to linear as in this invention disclosure in accordancewith on embodiment. Periodic arrangements of holes surrounding solid orhollow regions of the drawn sheet can result in photonic bandgapcreation and confinement of light. This can be used for flexiblewaveguides and interconnects that are sensitive to bending andmechanical forces. Structures can be designed and implemented tominimize the dependence of light guiding properties on bending andexternal stimuli for efficient light transport. Similarly, structurescan be designed and realized with high sensitivity to the ambient forsensing.

This method can also be used for reducing the effective refractive indexof film by introducing hollow capillaries considerably smaller thanlight (electromagnetic) wavelength range in question.

Holey Sheets Filled with Materials

Hollow capillaries (as explained above) can then be filled with liquidsor gases. They can even be filled liquid materials that solidify afterfilling and perhaps some processing. Examples of materials: solutionsincluding organic dyes for utilization of their fluorescence orabsorption that show different properties in the liquid phase than inthe solid phase. Liquid crystals and their mixtures can be used for manyapplications requiring switchable birefringence.

Holey sheets (either filled or not) can be used for bio-medical orchemical sensing applications. Structures, sizes and distances betweenhollow, solid or liquid-filled channels in a film can be adjusted anddesigned to enhance the light interaction from some channels withmaterial (specimens and liquid or gas samples) in other channels.

Opto-fluidic experiments and devices can be realized in the form offlexible sheets using this method of capillary production in sheets.

Transversely Elongated Fibers

If the aspect ratio of the preform is not large and the dimensions alongthe first and the second transverse directions are close the effect ofthe edges will dominate the effect of one-directional temperaturegradient. Therefore, preform shrinks in both transverse directions.Since the sources of heat are only on two sides of the preform, however,shrinkage ratio will be larger in that direction compared to that in thesecond direction. Therefore, the aspect ratio of the preform will changeduring the drawing. This way a square preform can be drawn into arectangular fiber, or a circular preform can be drawn into an ellipticalfiber which is otherwise difficult to make especially if ellipticalinternal features are needed in fiber.

A Method to Avoid Layer (Component) Delamination in Structured FilmsComposed of More than One Material

When the structured sheets (and therefore slab-like preforms) compriseof two or more materials that do not adhere together very well,component may separate or delaminate over time. For example, if thestructure has layers of two materials, layers may delaminate and developair gaps between them. Two methods to avoid this undesired effect aredescribed with reference to FIGS. 14-15.

When the structured sheets (and slab-like preforms) include two or morematerials that do not adhere together very well, components may separateor delaminate over time. FIGS. 14 and 15 demonstrate two alternatives toavoid delamination and separation of components in a multi-materialfilm. The multi-material features (3) of the film (1) can be split intodiscrete sections of multi-material features (3) to allow continuity ofthe majority material (2). Discrete multi-material features (3) may beseparated by horizontal gaps (6) of the majority material (1). Thecontinuity of the film majority material (2) is intended to maintain theintegrity of the film (1). Tension stored in the film during the sheetdrawing process is also intended to help maintaining the multi-materialcomponents in tight contact and to avoid delamination or separation.Discretization of the multi-material features can be achieved in atleast two ways, one with horizontal separation (FIG. 14) and one withvertical separation (FIG. 15). In the former case, horizontal spacing(6) between discrete multi-material features is intended to cause thesurrounding majority material (2) to be continuous. Material (2) in thehorizontal spacing may act as bridge between two sides (4, 5) of themulti-material features (3) and may force them to remain in tightcontact within the features and with the surrounding or outer material(2). In this embodiment, the area of the sheet on the top of bridgeareas (6) is optionally not covered by multi-material features (3).Total surface coverage may be beneficial to some applications of suchmulti-material films. For example, multi-layered films with spectrallyselective reflectivity for solar energy applications or for energyefficient window films may benefit from total surface coverage. For suchcases, discrete segments of the multi-material features can be arrangedin more than one horizontal plane and can be separated by verticalspacing (7), as shown in FIG. 15 instead of horizontal (FIG. 14).Preforms of such films with features separated vertically may befabricated in another manner.

FIG. 16 shows one embodiment for asymmetric drawing. Temperaturegradient “C” does not have to be symmetric across the thickness T1 ofthe slab-like preform. The material may be pulled from the line or pointof lowest temperature. If temperature distribution is symmetric acrossthe thickness T1, the film may be pulled from the central line ofsymmetry of the preform. Otherwise, the line of lowest temperature mayfall on one side of line of symmetry of the preform and film may bepulled from that location instead. In cases where the thickness of thepreform is not considerably large compared to that of the furnace, itmay be difficult to create enough temperature gradient between thesurrounding or outer surface of the preform (front and rear) and thecenter line of the preform. It is preferable to create a largetemperature gradient from one surface to another instead. Thus, in oneembodiment the film drawing may take place asymmetrically from a linecloser to one surface than to the other.

The plane at which the sheet is drawn is not required to be the centralplane of the furnace or preform. Film will start drawing down from theline of lowest temperature and highest viscosity. In asymmetric heating,one side of the slab-like preform is hotter than the other side. Thus,in one embodiment the line of film drawing is closer to the cold side ofthe furnace than to the hotter side.

In FIG. 16 one surface is heated lightly just to allow material flowwhile the other is applied more heat to create a large thermal gradient.In this case, film drawing takes place from a line close to one surfaceof the preform.

In both cases the layered (or the multi-material structured) section ofthe film is surrounded by a bulk of a uniform jacket material. The mainmatrix of the material that surrounds internal structures is drawn undertension together with the rest of the film and stores some tensionacross the thickness of the film (vertical here). This tension may keepthe layered (or multi-material components) sections sandwiched under atransverse pressure. It may be beneficial to leave some gaps betweenlayered (or multi-material structured) sections so that the continuityof the surrounding material helps the integrity of the film. In caseswhere such gaps are not proper for specific applications (for example,when it is necessary that the structured sections cover close to 100% ofthe film surface area), layered (or multi-material) sections can beplaced in different alternating levels (displaced vertically and/orhorizontally) so that the discontinuity in layers gives continuity tothe uniform surrounding material.

Stack-and-Draw Method for Structured Sheets

Stack and drawing is a known method in structured fiber fabrication. Dueto the limits in draw-down factor during a single drawing process, orlimits of a custom-design that requires different shrinkage ratios fordifferent elements in a preform, some elements of a fiber are firstdrawn down to an intermediate size (cane). They are then stacked andassembled into another preform together with other elements; and finallydrawn into a final structured fiber. The most common example is thefabrication of photonic crystal fibers. Cylindrical tubes are firstdrawn down by a few times to create intermediate-size capillaries socalled “Canes”. Canes are then stacked and placed in a tube and drawnagain into fibers. Finally, the capillaries are shrunk in size a fewtimes more than the outer tube, although they are drawn together at theend, because the capillaries have gone through an additional drawingstep prior to the final drawing

Such stack-and-draw method can be applied to the current invention ofsheet drawing. The only difference here is that elements can be drawndown only in one transverse direction in each draw. Since draw-downratio can be adjusted in each draw, one can define the difference in theaspect ratio change for the two orthogonal transverse directions in thefollowing way.

Example 1

Let's assume that one wants to draw a polymer or glass layer from 1 mmthickness to 100 nm. This film can be embedded into a slab-like preform.But it is not practical to drawn a preform down by 1000 times in onedraw. So, we can draw this preform once by a factor or F1, embed thedrawn film in a second slab-like preform, and draw it down by anotherfactor F2 in a way that F1*F2=1000.

Example 2

Let's assume one wants to have a periodic structure in a final filmwhose direction of periodicity (grating vector, in optics terms) isalong the transverse direction (width) W1 of the final film. We want theperiodic structure to have alternate layer thicknesses of 1 micrometerand 2 micrometers, and we want the final film to have a total thicknessof 0.1 mm. We can assemble a first slab-like preform that includes amulti-layer stack of the two materials with initial thicknesses 100micro-meters and 200 micro-meters, respectively. We can then draw thispreform down by 100 times so that bilayers have the target thicknessesof 1 micron and 2 microns. The direction of periodicity, however, isstill across the thickness of the first preform/film (T1 or T2). Then wecan cut the film along the longitudinal direction in pieces 10 mm wide,rotate (flip) them by 90 degrees and stack them in the direction ofpreform width (W). We can assemble (or embed) them into a second preformwhich is now 10 mm thick. This preform can be drawn down by a factor of100 to give a final film 0.1 mm thick with multi-layers than are shrunkin one direction, but not the other. Therefore, layers in the bilayersystem are drawn in one direction in the first draw, and in a seconddirection during the second draw.

Example 3

One can take the following steps to create a layered film with changinglayer thickness. Layers of different thicknesses can be stacked in theinitial preform before the preform is consolidated and drawn. However,this may not be very practical or efficient when complex layerstructures are desired or when layers in the preform level are supposedto be very thin and therefore difficult to handle. For example, discreterugate structures where each periodic cycle of refractive indexvariation is formed of several sub-layers each in the range of five tofifty nanometers. Such sub-layers should be sub-micrometer thick in thepreform level. A person of ordinary skill would recognize that handlingdelicate sub-micrometer films (if available in free standing form) isvery difficult. In such cases, one can instead obtain the final filmthrough two or more steps of stacking and re-drawing. As anotherexample, if a chirped layered structure is needed with final layerthicknesses ranging between 10 nm and 1 micron with smooth and gradualvariations, a single draw with a typical draw-down ratio of 100 willmandate layer thicknesses ranging gradually between 1 micron to 100microns in the preform level. While 100-micron films are easy to handleand feasible to obtain through currently available film productionmethods, 1-micron films are not. One can instead start with a preformassembled from layers between 100 microns and 1 mm. This first preformcan be drawn at two different draw-down ratios of 10 and 100corresponding to two different sets of drawing parameters during thesame drawing process of the same preform. The first part will give drawnlayers in the range 10 microns to 100 microns, while the second partwill give layers in the range 1 micron to 10 microns. Pieces from thesetwo parts can then be stacked to form a preform with layer thicknessescovering the entire range 1 micron to 100 microns. This second preform(once drawn by a ratio of 100) yields layer thicknesses in the range 10nm to 1 micron in a smooth and gradual manner.

Example 4

Films with periodic variation in layer properties such as thickness orrefractive index can be made the following way. One half of a cycle ofthe periodic variation can be made through stacking of several layerswith properly designed and selected layers into one preform. This firstpreform can then be drawn into extended length of film with anintermediate thickness. Pieces of this film can be cut, flipped andstacked as many times as needed to create a second preform with severalcyclic variations in the properties of layers across the preformthickness. This second preform can then be drawn into a final film withseveral cycles of layer variation with the final target thicknesses.Alternatively, the first preform can be drawn into intermediate filmswith different thicknesses. Therefore, stacking pieces from varioussections of the first drawn film will result in a second preform withcyclic variations of layers and varying periodicity of cycles across thepreform thickness. This second preform, when drawn down to a film, willinclude cyclic variations with varying periodicities. If the varyingproperty in layers is the optical refractive index, final films madethis way are rugate filters with periodic variation of refractive indexacross the film thickness, and varying periodicities that allow for finetuning of reflection bandwidth and band center in their opticalreflection spectrum.

This method of multi-layer film manufacturing with either one-stepdrawing or stack-and-draw process may be used for adjusting theeffective refractive index of film material by combining layers orfeatures of at least two materials with different refractive indiceswith final dimensions considerably smaller than light (electromagnetic)wavelength of interest for specific applications.

Since many modifications, variations, and changes in detail can be madeto the described preferred embodiments of the invention, it is intendedthat all matters in the foregoing description and shown in theaccompanying drawings be interpreted as illustrative and not in alimiting sense. Thus, the scope of the invention should be determined bythe appended claims and their legal equivalents.

What is claimed is:
 1. A method of drawing a material into sheet form,the method comprising the steps of: providing a preform comprising atleast one material wherein a first transverse dimension of the preformis greater than a second transverse dimension that is substantiallyperpendicular to the first transverse dimension, the preform also havinga third dimension that is substantially perpendicular to the first andsecond transverse dimensions and defining a pulling direction; providinga furnace having at least one heating element on at least one side ofthe furnace; energizing the at least one heating element to apply heatto the preform, without the at least one heating element physicallycontacting the preform, only along an exterior surface of the firsttransverse dimension to create a thermal gradient of decreasingtemperature from the exterior surface inward along the second transversedimension toward a plane of the preform, wherein the at least oneheating element creates approximately uniform temperature distributionalong the first transverse dimension; feeding the preform into thefurnace; and drawing, by pulling in the pulling direction, the preformin such a manner that the material does not substantially deform acrossits first transverse dimension and deforms across its second transversedimension while stretching the preform in the third dimension.
 2. Themethod of claim 1, further comprising preheating the at least onematerial before the at least one material enters a hottest zone of thefurnace and further heating the at least one material after it leavessaid hottest zone to gradually bring said at least one material to alower temperature.
 3. The method of claim 1, wherein heating is appliedapproximately symmetrically along the second transverse dimension. 4.The method of claim 1, wherein the at least one material comprises atleast one of a thermoplastic polymer, any type of glass, amorphousmaterials that can be stretched when heated, and metals.
 5. The methodof claim 1, wherein the preform comprises two or more materials withsimilar thermal and mechanical properties.
 6. The method of claim 1,wherein the step of providing a preform comprises providing a firstblock comprising a first material and embedding in the first block asecond block of a second material; wherein, upon completion of thedrawing step, the sheet form comprises layers corresponding to saidfirst and second materials.
 7. The method of claim 1, wherein the stepof providing a preform comprises providing a first block comprising afirst material and embedding in the first block parallel layers ofdifferent materials or identical materials with different dopants;wherein, upon completion of the drawing step, the sheet form compriseslayers corresponding to said first material and said different materialsor identical materials with different dopants.
 8. The method of claim 1,wherein the step of providing a preform comprises providing a firstblock comprising a first material and embedding in the first block aplurality of vertically aligned secondary material elements centered ona vertical axis of the preform; wherein, upon completion of the drawingstep, the sheet form comprises layers corresponding to said firstmaterial and said plurality of vertically aligned secondary materialelements.
 9. The method of claim 1, wherein the step of providing apreform comprises providing a first block comprising a first materialand embedding in the first block a plurality of parallel alignedsecondary material elements; wherein, upon completion of the drawingstep, the sheet form comprises layers corresponding to said firstmaterial and said plurality of parallel aligned secondary materialelements.
 10. The method of claim 1, wherein the first transversedimension of the preform is at least 1.5 times greater than the secondtransverse dimension.
 11. The method of claim 1, wherein the firsttransverse dimension of the preform is at least five times greater thanthe second transverse dimension.
 12. The method of claim 1, wherein thefirst transverse dimension of the preform is at least ten times greaterthan the second transverse dimension.
 13. The method of claim 1, whereinthe step of providing a furnace comprises providing a plurality ofheating elements on one, or both, sides of the furnace, wherein theplurality of heating elements are along opposite exterior surfaces ofthe first transverse dimension to create a temperature gradient in onedirection inward from one of the exterior surfaces along the secondtransverse dimension towards a plane of the preform that is larger thana temperature gradient in another direction inward from the opposingexterior surface along the second transverse dimension towards the planeof the preform to cause asymmetric drawing.
 14. The method of claim 1,wherein the first transverse dimension of the preform is at least onethousand times greater than the second transverse dimension.